Quantumness, Randomness and Computability

Solís, Aldo; Hirsch, Jorge G.

doi:10.1088/1742-6596/624/1/012001

Cited by 1 publication

(1 citation statement)

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“…Indeed, as von Neumann noted, 'there is no such thing as a random number-there are only methods to produce random numbers ' [29]. The insight of von Neumann is not that the algorithmic notion of randomness is problematic-indeed, it is highly satisfactory as a notion of random objects-but that there is a dual concept of randomness, that of random processes [28,30,31]. Such a concept has historically received little attention, but the most convincing attempts to make it rigorous are perhaps those which define it as a form of maximal unpredictability: the outcome of such a process should be unpredictable for any physical observer [32,33].…”

Section: Randomnessmentioning

confidence: 99%

Experimentally probing the algorithmic randomness and incomputability of quantum randomness

et al. 2019

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The advantages of quantum random number generators (QRNGs) over pseudo-random number generators (PRNGs) are normally attributed to the nature of quantum measurements. This is often seen as implying the superiority of the sequences of bits themselves generated by QRNGs, despite the absence of empirical tests supporting this. Nonetheless, one may expect sequences of bits generated by QRNGs to have properties that pseudo-random sequences do not; indeed, pseudorandom sequences are necessarily computable, a highly nontypical property of sequences.In this paper, we discuss the differences between QRNGs and PRNGs and the challenges involved in certifying the quality of QRNGs theoretically and testing their output experimentally. While QRNGs are often tested with standard suites of statistical tests, such tests are designed for PRNGs and only verify statistical properties of a QRNG, but are insensitive to many supposed advantages of QRNGs. We discuss the ability to test the incomputability and algorithmic complexity of QRNGs. While such properties cannot be directly verified with certainty, we show how one can construct indirect tests that may provide evidence for the incomputability of QRNGs. We use these tests to compare various PRNGs to a QRNG, based on superconducting transmon qutrits and certified by the Kochen-Specker Theorem, to see whether such evidence can be found in practice.While our tests fail to observe a strong advantage of the quantum random sequences due to algorithmic properties, the results are nonetheless informative: some of the test results are ambiguous and require further study, while others highlight difficulties that can guide the development of future tests of algorithmic randomness and incomputability.1 An example is the discovery in 2012 of a weakness in the encryption system used worldwide for online shopping, banking and email; the flaw was traced to the numbers a PRNG had produced [1]. As of 2018, Java still relies on a linear congruential generator, a low quality PRNG.arXiv:1806.08762v2 [quant-ph]

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